{
  "id": "0808.3656",
  "version": "v1",
  "published": "2008-08-27T09:01:58.000Z",
  "updated": "2008-08-27T09:01:58.000Z",
  "title": "Martingale approach to stochastic differential games of control and stopping",
  "authors": [
    "Ioannis Karatzas",
    "Ingrid-Mona Zamfirescu"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/07-AOP367 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2008, Vol. 36, No. 4, 1495-1527",
  "doi": "10.1214/07-AOP367",
  "categories": [
    "math.PR"
  ],
  "abstract": "We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate conditions, we show that the game has a value and construct a saddle pair of optimal control and stopping strategies. Crucial in this construction is a characterization of saddle pairs in terms of pathwise and martingale properties of suitable quantities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-27T09:01:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E20",
      "60G40",
      "91A15",
      "91A25",
      "60G44"
    ],
    "keywords": [
      "martingale approach",
      "studying continuous-time stochastic differential games",
      "saddle pair",
      "martingale properties",
      "optimal control"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.3656K"
    }
  }
}